Diminished value, I believe, might be looked at differently, depending on what state you live in. Here in Georgia, it's virtually automatic. Don't have to ask for it. My car was hit (not my fault), other drivers insurance company paid, no problem. Received a check about two weeks after the repair. Never had to ask for it.
And yes, two vehicles of equal quality, one accident free, the other with reported accident, the value of the accident free vehicle will be higher. Higher trade in, higher resale, etc..
As far as private sellers having to disclose all accidents (by law), have no clue how people can make this stuff up and believe it.
Mike